Firstly, it assumes that code is valuable in of itself. But code is a liability, not an asset. Removing code while maintaining functionality creates value because it improves agility without costing anything that stakeholders care about.

Secondly, it assumes that code/functionality is the only purpose of development. But agile practitioners use development as a way of gaining information. So even if a change is fully backed-out and never restored, the process of developing that change yielded an improved understanding of the solution space.

I realise that deconstructing fallacies is somewhat of a fallacy itself. Counterproductive practices are more likely to be driven by psychological factors than by logical errors. In this case, I think that a reluctance to delete code is motivated by an attitude I call the waterfall mindset.

Within the waterfall mindset, coding proceeds through a series of decisions that are never revisited once made. It's very similar to a sequential development process, except that the phases can be in the mind of a single developer. Like normal waterfall development, it relies on the supremely unlikely possibility of getting decisions right the first time:

Generating reports is too slow? Let's cache them on the webserver.

Cached files are out of date? Let's write a cron job to renew them every night.

The webserver is under unacceptable load during the regeneration process? Let's delegate to a separate report server.

Report generation fails silently when there are network problems? Let's develop a custom protocol with failure semantics so that the webserver knows when to re-send messages to the report server.

And so on...

Or perhaps the report generation process itself could be profiled and optimised, eliminating the need for a caching mechanism altogether.